1. Various Mostly Lagrangian Things Mark Neyrinck Johns Hopkins University Collaborators: Bridget Falck, Miguel Aragón-Calvo, Xin Wang, Donghui Jeong, Alex Szalay Tracing the Cosmic Web, Leiden, Feb 2014

2. Mark Neyrinck, JHU Outline Comparison in Lagrangian space Comparison in Lagrangian space Halo spins in an origami model Halo spins in an origami model Lagrangian substructures Lagrangian substructures Incorporating rotation into a velocity-field classification Incorporating rotation into a velocity-field classification Halo bias deeply into voids with the MIP Halo bias deeply into voids with the MIP

3. Mark Neyrinck, JHU Information, printed on the spatial “sheet,” tells it where to fold and form structures. 200 Mpc/h

4. Why “folding?” In phase space... (e.g. analytical result in Bertschinger 1985) Mark Neyrinck, JHU

5. N-body cosmological simulation in phase space: a 2D slice Mark Neyrinck, JHU x vxvx y x z y

6. Eric Gjerde, origamitessellations.com Rough analogy to origami: initially flat (vanishing bulk velocity) 3D sheet folds in 6D phase space. - The powerful Lagrangian picture of structure formation: follow mass elements. Particles are vertices on a moving mesh. - Eulerian morphologies classified by Arnol’d, Shandarin & Zel’dovich (1982) - See also Shandarin et al (2012), Abel et al. (2012) …

7. (Neyrinck 2012; Falck, Neyrinck & Szalay 2012) The Universe’s crease pattern Crease pattern before folding After folding

8. Mark Neyrinck, JHU Web comparison in Lagrangian coordinates Warming up: Lagrangian → Eulerian → Lagrangian for ORIGAMI

9. Mark Neyrinck, JHU Web comparison in Lagrangian coordinates ORIGAMI

10. Mark Neyrinck, JHU Web comparison in Lagrangian coordinates Forero & Romero

11. Mark Neyrinck, JHU Web comparison in Lagrangian coordinates Nuza, Khalatyan & Kitaura

12. Mark Neyrinck, JHU Web comparison in Lagrangian coordinates NEXUS+

13. Flat-origami approximation implications: - # of filaments per halo in 2D: generically 3, unless very special initial conditions are present. - # of filaments per halo in 3D: generically 4. Unless halo formation generally happens in a wall Assumptions: no stretching, minimal #folds to form structures

14. Flat-origami approximation implications: Galaxy spins? To minimize # streams, haloes connected by filaments have alternating spins Are streams minimized in Nature? Probably not, but interesting to test. A void surrounded by haloes will therefore have an even # haloes — before mergers

15. Chirality correlations Connect to TTT (tidal torque theory): haloes spun up by misaligned tidal tensor, inertia tensor. Expect local correlations between tidal field, but what about the inertia tensor of a collapsing object? - Observational evidence for chiral correlations at small separation (… Pen, Lee & Seljak 2000, Slosar et al. 2009, Jiminez et al. 2010)

16. ORIGAMI halo spins in a 2D simulation Galaxy spins? To minimize # streams, haloes connected by filaments have alternating spins A void surrounded by haloes will therefore have an even # haloes

17. Mark Neyrinck, JHU Lagrangian slice: initial densities

18. Mark Neyrinck, JHU Lagrangian slice: VTFE* log-densities *Voronoi Tesselation Field Estimator (Schaap & van de Weygaert 2000)

19. Mark Neyrinck, JHU Lagrangian slice: LTFE* log-densities Halo cores fairly good-looking! *Lagrangian Tesselation Field Estimator (Abel, Hahn & Kahler 2012, Shandarin, Habib & Heitmann 2012)

20. Mark Neyrinck, JHU Lagrangian slice: ORIGAMI morphology node filament sheet void

21. LTFE in Lagrangian Space — evolution with time

22. Mark Neyrinck, JHU “Time spent as a filament/structure” map

23. Morphologies with rotational invariants of velocity gradient tensor Slides from Xin Wang

24. SN-SN-SN (halo)UN-UN-UN (void)SN-S-S (filament)UN-S-S (wall) 1Mpc/h Gaussian filter, using CMPC 512 data SFSSFCUFSUFC both potential & rotational flow Slides from Xin Wang

25. Stacked rotational flow from MIP simulation Slides from Xin Wang

26. Halo bias deeply into voids without stochasticity/discreteness with Miguel’s MIP simulations Mark Neyrinck, JHU MN, Aragon-Calvo, Jeong & Wang 2013, arXiv:1309.6641

27. Comparison of: Halo-density field with Halo-density field predicted from the matter field Mark Neyrinck, JHU Not much environmental dependence beyond the density by eye!

28. “Conclusion” Visualization of the displacement field Mark Neyrinck, JHU